Gleason-Type Theorems from Cauchy’s Functional Equation

Abstract

Gleason-type theorems derive the density operator and the Born rule formalism of quantum theory from the measurement postulate, by considering additive functions which assign probabilities to measurement outcomes. Additivity is also the defining property of solutions to Cauchy’s functional equation. This observation suggests an alternative proof of the strongest known Gleason-type theorem, based on techniques used to solve functional equations.

Metadata

Item Type:	Article
Authors/Creators:	Wright, Victoria J Weigert, Stefan https://orcid.org/0000-0002-6647-3252
Copyright, Publisher and Additional Information:	Funding Information: VJW gratefully acknowledges funding from the York Centre for Quantum Technologies and the WW Smith fund. Publisher Copyright: © 2019, The Author(s).
Keywords:	Axioms of quantum theory,Born rule,Density operators,Functional equations,Gleason’s theorem,POVMs
Dates:	Accepted: 29 May 2019 Published (online): 4 June 2019 Published: 15 June 2019
Institution:	The University of York
Academic Units:	The University of York > Faculty of Sciences (York) > Mathematics (York)
Depositing User:	Pure (York)
Date Deposited:	05 Jun 2019 12:10
Last Modified:	09 Apr 2025 23:22
Published Version:	https://doi.org/10.1007/s10701-019-00275-x
Status:	Published
Refereed:	Yes
Identification Number:	10.1007/s10701-019-00275-x
Related URLs:	http://www.scopus.com/inward/record.url?... https://arxiv.org/abs/1905.12751
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:146960

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Gleason-Type Theorems from Cauchy’s Functional Equation

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